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Consider two bodies orbiting each other.

As the Universe expands would the distance between them increase?

Most people say that a gravitationally bound system will not expand with the Universe. They say that such a system is not described by the FRW solution.

But surely one could consider two orbiting bodies that are sufficiently far away that the spacetime between them could be approximately described by the FRW solution? In this case the recession velocity would be of the same order as the orbit velocity.

Qmechanic
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John Eastmond
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    Answers will essentially be duplicates of http://physics.stackexchange.com/q/2110/2451 and links therein. – Qmechanic Apr 16 '13 at 16:41
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    @Qmechanic I think that question and its links are all focused on expansion vs. electromagnetism, whereas this is gravity vs. gravity, so it's a somewhat different beast of a question (even if the answers run parallel). –  Apr 16 '13 at 16:51
  • @ChrisWhite I remember answering a question very close to this (and not the one that Qmechanic links), but I"m too lazy to look it up right now, too. – Zo the Relativist Apr 16 '13 at 16:57

2 Answers2

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The short answer is that cosmic expansion can affect orbits, but the actual effect is completely undetectable for solar system parameters (I think it was below machine error when I did it numerically). For sufficiently large cosmic expansions, you actually don't even have stable orbits anymore.

There are a large number of potential models to describe asymptotically FRLW black hole spacetimes, and it is somewhat unclear which model is the correct choice. I can point you to references if you wish.

Zo the Relativist
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  • Thanks for the answer. I suppose I was thinking in a naive way that Newtonian attraction causes the two bodies to accelerate towards each other whereas Hubble expansion causes them to have a relative velocity. I thought perhaps a solution would be a simple sum of these two effects. – John Eastmond Apr 16 '13 at 17:25
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There are two essentially different effects at work with gravitational orbits in an expanding space-time. Gravity is a force, or acceleration field while expansion is a velocity or drift field. It is difficult to combine them into a single equation.

At close distances expansion is very small and has very little effect on the orbit of a planet. As the distance between the central mass and the satellite increases the force of gravity declines while the drift of expansion increases. At great distances, orbital velocities will slow due to expansion until the satellite becomes unbound to the central mass.

I wish I had a good reference for mathematical treatment of gravitational orbits in an expanding space-time. Someone out there must have worked out this problem.

John Huenefeld
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